Question

eliminate the parameters of the parametric equations x=3+6 cos t and y= 6+6 sin t

Answer 1

x = 3 + 6cost
6cost = x-3
cost = (x-3)/6
similarly , from the 2nd equation
sint = (y-6)/6

but we know, sin^2 t + cos^2 t = 1

( (y-6)/6)^2 + ( (x-3)/6)^2 = 1
(x-3)^2 /36 + (y-6)^2/36 = 1

(x-3)^2 + (y-6)^2 = 36

you should recognize that as a circle with radius of 6 and centre (3,6)